Characterising the temporal variability of the spatial distribution of animals: an application to seabirds at sea

Understanding the patterns of spatial and temporal variations in animal abundance is a fundamental question in ecology. Here, we propose a method to quantify temporal variations in animal spatial patterns and to determine the spatial scale at which such temporal variability is expressed. The methodology extends from the approach proposed by Taylor (Taylor, L. R. 1961. Aggregation, variance and the mean. Nature 189: 732-735) and relies on models of the relationship between temporal mean and variance in animal abundance. Repeated observations of the spatial distribution of populations are used to construct spatially explicit models of Taylor's power law. The resulting slope parameters of the Taylor power law provide local measures of the temporal variability in animal abundance. We investigate if the value of the slope varies significantly with spatial location and with spatial scale. The method is applied to seabirds distribution in the Bay of Biscay. We study four taxa (northern gannets, large gulls, auks and kittiwakes) that display distinct geographical distribution, spatial structure and foraging strategy. Our results show that the temporal variability associated to the spatial distribution of northern gannets is high and spatially homogeneous. By contrast, kittiwakes present large geographical areas associated with high and low variability. The temporal variability of auk's spatial distribution is strongly scale-dependent: at fine scale high variability is associated to high abundance, but at large scale high variability is associated to the external border of their distribution range. The method provides satisfactory results and useful information on species spatio-temporal distribution.